Question

practice describing congruent angle relationships
study the example showing how to use angle relationships to find unknown angle measures. then solve problems 1 - 6.
example
what is the value of x?
bd and eg are parallel, so corresponding angles are congruent.
25x - 2 = 148
25x = 150
x = 6
a. in the example, what angle forms a pair of alternate - interior angles with ∠cfg?
b. what is the measure of the angle you named in problem 1a?
what is the value of x? show your work.
4x°
140°
describe a sequence of transformations you can use to show ∠jlk ≅ ∠qnr.

Explanation:

Step1: Recall alternate - interior angles property

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. In the given example with parallel lines \(BD\) and \(EG\) cut by transversal \(AH\), \(\angle CFG\) and \(\angle BCF\) are alternate - interior angles.

Step2: Find the measure of \(\angle BCF\)

Since \(\angle CFG = 148^{\circ}\) and \(\angle BCF\) is congruent to \(\angle CFG\) (alternate - interior angles), the measure of \(\angle BCF\) is \(148^{\circ}\).

Step3: Solve for \(x\) in the new angle - pair

For the pair of angles \(4x^{\circ}\) and \(140^{\circ}\), if they are corresponding angles (assuming the lines are parallel), then \(4x=140\). Divide both sides of the equation by 4: \(x = \frac{140}{4}=35\).

Answer:

a. \(\angle BCF\)
b. \(148^{\circ}\)
c. \(x = 35\)